South Carolina Alternate Assessments Performance Level Descriptors Mathematics Revised: June 29, 2018 Contents Standards Reference Number Abbreviations... 1 Grade 3... 2 Grade 4... 6 Grade 5... 9 Grade 6... 13 Grade 7... 17 Grade 8... 21 Grade 11... 24
Standards Reference Number Abbreviations Number Sense and Base Ten (NSBT) Number Sense Fractions (NSF) Algebraic Thinking and Operations (ATO) Geometry (G) Measurement and Data Analysis (MDA) The Number System (NS) Ratios and Proportional Relationships (RP) Expressions, Equations, and Inequalities (EE) Geometry and Measurement (GM) Data Analysis and Statistics (DS) Fractions (F) Arithmetic with Polynomials and Rational Expressions (AAPR) Creating Equations (ACE) Reasoning with Equations and Inequalities (AREI) Structure and Expressions (ASE) Interpreting Functions (FIF) Quantities (NQ) Real Number System (NRNS) Interpreting Data (SPID) Page 1
Grade 3 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 3.NSBT.1 Round whole numbers up to 100 to the nearest 10. 3.NSBT.2 Add and subtract single-digit numbers. 3.NSBT.3 Multiply one-digit whole numbers by 10. NSBT 3.4 Read numbers up to 999. 3.NSBT.5 Compare and order numbers up to 999 using the symbols >, =, or <. 3.NSF.1 Develop an understanding of fractions (i.e., denominators 2, 3, 4, 6, 8, 10) as numbers. Recognize a unit in the place value system (limited to ones and tens place values). Recognize the addition, subtraction, and equal signs. Recognize the numbers 1 10 as a set for the tens place. Identify numbers in word form (limit to numbers 1 50) Recognize the <, >, and = signs. Identify a fraction from a list of numbers (i.e., 3 choices, 2 whole numbers, and 1 fraction) Understand the point when a number should be rounded up (limited to numbers from 1 10). Identify the functions of addition, subtraction, and equal signs (limited to numbers 1 5). Identify sets of numbers in tens using numbers 1 30. Identify numbers in word form (numbers ranging from 1 50) Arrange a set of numbers from least to greatest. Identify parts of a fraction (denominator/numerator). Round whole numbers from 0 30 to the nearest 10. Demonstrate the concept of addition and subtraction (limited to single digit numbers from 1 10). Demonstrate the concept of counting by 10 by counting the sets of 10 and adding a zero to the end of number of sets (limited to the numbers 1 50). Identify numbers in word form (numbers ranging from 1 100 ) Compare 2 numbers up to 50 using symbols (=, <, >). Identity a part of a whole using fraction models. Round whole numbers from 0 100 to the nearest 10. Determine the unknown in an addition/subtraction equation. Count by tens starting at a multiple of 10 (using a set of 10 objects, numbers, etc., e.g., count with dimes). Read numbers up to 999. Compare 2 numbers up to 100 using symbols (=, <, >). Match fractions to their models (i.e. denominators limited to 2, 3, 4, 6, 8, 10). Page 2
3.NSF.2 Explain fraction equivalence (i.e., denominators 2, 3, 4, 6, 8, 10) by demonstrating an understanding that two fractions are equal if they are the same size, based on the same whole, or at the same point on a number line. 3.ATO.1 Use concrete objects, drawings and symbols to represent multiplication facts of two single-digit whole numbers (i.e., 0 5). 3.ATO.3 Solve real-world problems involving equal groups, area/array, and number line models using basic multiplication (i.e., 0 5). 3.ATO.4 Determine the unknown whole number in a multiplication equation relating three whole numbers when the unknown is a missing factor or product. Identify shapes divided into equal parts. Identify the multiplication symbol. Recognize a group, an array, and a number line using models or pictures. Identify the key terms, factor/product, in a multiplication equation. Identify fraction models that are divided into the same number of parts. Demonstrate the concept of multiplication by using the repeated addition strategy (limiting the numbers to 0 2). Match a basic multiplication expression with its model. Determine the unknown whole number in a multiplication equation by selecting the missing product from a set of whole numbers (limiting the numbers 0 5). Recognize that two fractions are equal if they are the same using different numbers in the denominators (using pictures limiting the denominators to 2, 3, and 4). Demonstrate the concept of multiplication using the multiplication sign using numbers (limiting numbers 0 3). Apply the concept of multiplying using equal groups by solving a simple word problem limiting the numbers from 0 5. Determine the unknown whole number in a multiplication equation by selecting the missing factor from a set of whole numbers (one missing factor between the numbers 0 5). Identify equal fractions that are the same size but have different fraction sizes using models and numbers to show fractions using the denominators 2, 3, 4, 6, 8, 10. Multiply two single digit whole numbers using 0 5. Solve a real-world problem using basic multiplication with equal groups, arrays, and/or the number line. Determine the unknown whole number in a multiplication equation by selecting the missing factor and product from a set of whole numbers (limiting the numbers 0 5). Page 3
3.ATO.5 Apply the Commutative Property of Multiplication. 3.ATO.7 Demonstrate basic multiplication facts of products through 25. 3.ATO.8 Solve one-step, real-world problems using addition and subtraction of whole numbers and having whole number answers. 3.ATO.9 Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, 10, and 25, up to a 100. 3.G.1 Recognize rhombuses, rectangles, and squares as quadrilaterals. 3.G.2 Partition twodimensional shapes into two parts with equal areas. 3.MDA.1 Use analog and digital clocks to record time to the nearest hour and a half using a.m. and p.m. Identify multiplication problems. Recognize basic multiplication sets (limited to the multiples of 0, 1 and 2). Recognize one-step equations. Match a basic multiplication expression with its model. Demonstrate the concept of multiplication by using pictures of group members being distributed a set number of items. Demonstrate addition/subtraction problems using manipulatives. Match equivalent multiplication expressions using models. Demonstrate the concept of multiplication by matching pictures of multiplication to the correct multiplication equation (limit the factors to between 0 and 5). Determine the unknown in an addition/subtraction equation. Count by 1, 2, and 5. Count by 10s. Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, and 10. Identify sides or angles of a quadrilateral. Identify two-dimensional shapes Identify a clock as a tool to measure time. Identify quadrilaterals. Recognize the equal parts of a two-dimensional shape. Match the time to an activity from a list. Recognize rhombuses, rectangles, and squares as quadrilaterals. Recognize one half on an area model. Use analog and digital clocks to record time to the nearest hour and half hour using a.m. and p.m. Demonstrate the understanding of the concept by filling in the missing factors in a commutative property equation (filing in one missing factor from both sides). Demonstrate basic multiplication facts of products through 25. Solve addition/subtraction word problems (limit the products to up to 10). Identify a rule for an arithmetic pattern limited to multiples of 1, 2, 5, 10, and 25, up to a 100. Identify all attributes of quadrilaterals (i.e. 4 sides, 4 angles). Recognize when a shape is not equal to one half. Demonstrate the concept of telling time to the half hour on both types of clocks. Page 4
3.MDA.2 Measure liquid volumes (capacity) in customary units (i.e., c., pt., qt., gal.) and metric units (i.e., ml, L) to the nearest whole unit. 3.MDA.3 Interpret data from a picture graph and a bar graph. 3.MDA.4 Measuring length to the nearest inch. Identify three-dimensional shapes. Identify a bar graph. Identify shapes that can have volume. Identify information from a bar graph. Demonstrate the concept by choosing the appropriate volume unit for given substance to be measured (i.e. what is the best unit to measure for a box of cereal?) Identify information from a picture graph. Identify a ruler. Identify an inch on a ruler. Recognize inches as a measure of length. Demonstrate the concept by choosing the appropriate volume unit for various given substance to be measured. Interpret data from a picture graph and a bar graph. Measuring length to the nearest inch. Page 5
Grade 4 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 4.NSBT.2 Recognize mathematical periods through 999,999. 4.NSBT.3 Round whole numbers up to 1000 to the nearest 10 or 100. 4.NSBT.4 Add and subtract two-digit whole numbers. 4.NSBT.5 Demonstrate basic multiplication facts of products through 100. 4.NSBT.6 Divide up to a twodigit dividend by a one-digit divisor without remainders using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division (excluding long division). 4.NSF.1 Using visual fraction models, recognize equivalent fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). Recognize the word form for numbers through 9. Recognize a place value unit. Recognize the addition or subtraction symbols. Recognize multiplication factors and products. Recognize the division sign. Identify a fraction from a whole number. Recognize word form for numbers through 99. Identify when a number can be rounded up to the nearest unit. Add/subtract two-digit whole numbers within 20. Demonstrate the concept of multiplication. Identify the components of a division problem (i.e. What is the dividend? What is the divisor? What is the quotient?). Identify models that have been divided in half or equal parts (i.e. denominators limited to 2 10) Recognize word form for numbers through 999. Round whole numbers from 0 30 to the nearest 10. Add/subtract within 100 with a two-digit number and a multiple of 10. Multiply two single-digit whole numbers using 0 5. Demonstrate the concept of division using manipulatives to divide into equal groups. Using same-size models that have been divided differently to solve equivalent fraction problems (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, and 25). Recognize word form for numbers through 999,999. Round whole numbers 0 100 to the nearest 10 or nearest 100. Solve addition/subtraction word problems within 100. Multiply two whole numbers using 0 10. Solve a division word problem using a two-digit dividend by a one-digit divisor. Using same-size models that have been divided differently to solve equivalent fraction problems. (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). Page 6
4.NSF.2 Compare two given fractions (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) with common denominators using the symbols >, =, or <. 4.NSF.3 Develop an understanding of addition and subtraction of fractions with a common denominator (i.e., denominators 2, 3, 4, 5, 6, 8, 10, 12, 25, 100) based on unit fractions. a. Develop an understanding of mixed numbers. 4.NSF.5 Express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and use this technique to add two fractions with respective denominators of 10 and 100. 4.NSF.6 Write a fraction with a denominator of 10 or 100 using decimal notation. 4.NSF.7 Compare decimal numbers to hundredths using visual models. Recognize greater than and less than signs. Identify common denominators in fractions. Recognize part of a whole using models. Identify where a decimal point is on the place value chart. Identify the tenths and hundredths place on the value chart. Recognize greater than, less than, and equal signs. Demonstrate the concept of greater than and less than using models/groups of manipulatives to choose which ones has more, less or equal (<,>, =). Identify numerators and denominators in fractions. Given a model, recognize tenths/hundredths using a model. Demonstrate the function of a decimal point as it represents a fraction using a place value chart. Demonstrate the function of a decimal point as it represents a fraction using a place value chart. Compare two fractions with like denominators using a pictorial model (=, <, >). Using simple fractions with common denominators (limited between the numbers 2 9); add or subtract the numerators in the fraction. Identify when two fractions are equivalent with the denominators of 10 and 100. Write a fraction from a decimal notation with the denominator of 10. Using visual models, compare decimals to hundredths place. Compare two fractions with like denominators (=, <, >). Add/subtract fractions with common denominators (denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, 25, 100). Develop an understanding of mixed numbers. Identify fractions with the denominators of 10 and 100 when comparing two fractions. Write a fraction with denominator of 10 or 100 as a decimal. Compare decimal numbers to hundredths place. Page 7
4.ATO.2 Solve one-step, real-world problems using basic multiplication (0 10) or division (with no remainders). 4.ATO.4 Find all factor pairs for whole numbers 1 24. Identify the components of a multiplication problem. Recognize what a factor pair is for a whole number. Demonstrate the concept of multiplication/division. Identify factors for whole numbers 1 5. Determine the unknown in multiplication/division equation. Identify factors for whole numbers 1 10. Solve one-step multiplication or division word problems. Identify factors for whole numbers 1 24. 4.ATO.5 Given the rule for a pattern, determine the next term in the sequence/pattern. 4.G.1 Identify points, line segments, and angles in two-dimensional figures. 4.G.2 Identify parallel and perpendicular lines. Recognize patterns. Recognize a point. Identify lines. Identify symbolic, repeating, and pictorial patterns. Identify a line or line segment. Identify shapes with parallel lines. Given the rule, determine the next term in a picture pattern/sequence. Recognize different types of angles (acute, right, obtuse and straight). Identify parallel and perpendicular lines. Given the rule, determine the next term in a number pattern/sequence. Recognize angle, point, or line segment in a twodimensional figure. Identify parallel and perpendicular lines in shapes. 4.MDA.1 Distinguish measurements within a single system of measurement customary (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, g, kg, ml, L) as larger or smaller. 4.MDA.3 Find the area and perimeter for rectangles when given the side lengths. 4.MDA.8 Determine the value of a collection of coins and bills greater than $1. Compare two pieces of data with the same unit of measurement. Distinguish between systems of measurement. Determine if measurements within one system are larger or smaller (i.e. in., ft., min., hr., ml, L). Recognize side lengths. Recognize a rectangle. Find area and perimeter by counting squares. Recognize money. Identify a penny, a nickel, a dime, and a quarter. Identify the value of a penny, a nickel, a dime, and a quarter. Compare the size of measurements within one system measure (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, g, kg, ml, L). Find area and perimeter for rectangles when given the side lengths. Determine the value of a collection of coins and bills greater than $1. Page 8
Grade 5 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 5.NSBT.2 Use whole number exponents to explain patterns in the number of zeroes of the product when multiplying a number by powers of 10. 5.NSBT.3 Read and write decimals in standard form. Compare two decimal numbers to the hundredths using the symbols >, =, or <. 5.NSBT.4 Round decimals to the nearest whole number. 5.NSBT.5 Multiply a multidigit whole number by a one-digit whole number using strategies to include a standard algorithm. 5.NSBT.6 Divide up to a four-digit dividend by a onedigit divisor, using strategies based on place value, the properties of operations, and the relationship between multiplication and division. Identify or continue a pattern. Recognize larger, smaller, and equal. Multiply a product of 10 by 10. Identify and define a decimal. Identify the product, given the number 10, with an exponent. Compare two decimals to the hundredths (=, <, >). Identify a unit. Identify a decimal Round a decimal to the nearest whole number (limit to decimals over 0.50). Identify and represent repeated addition with an equation. Identify equal groups. Solve repeated addition problems. Understand that equal group can be represented by division. Demonstrate the concept of multiplication related to repeated addition. Apply the relationship between multiplication and division. Identify the power of 10, given the product. Compare two decimals to the hundredths (=, <, >). Read and write monetary values. Round a decimal to the nearest whole number. Multiply by 1, 2, 3, 4, and/or 5. Divide by 1, 2, 3, 4, and/or 5. Page 9
5.NSBT.7 Add and subtract decimal numbers to hundredths using concrete area models and drawings. 5.NSF.1 Add and subtract fractions with unlike denominators using a variety of models, including an area model and number line. 5.NSF.4 Multiply a whole number by a fraction. 5.ATO.1 Evaluate two-step numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces). 5.ATO.2 Translate verbal phrases into simple numerical expressions. 5.G.1 Define a coordinate system. Identifies whole and part. Partition any shape into equal parts. Add two of the same fraction (limit to halves, thirds, fourths). Identify grouping symbols in an expression (parentheses, brackets, braces). Identify the symbol that correlates with sum, product, take away, divide. Recognize point on a number line (limit to numbers greater than 0). Identify a whole number when presented in monetary form. Identify a decimal when presented in monetary form. Create a model of a fraction (partition and shade). Understand the relationship between adding and multiplying the fraction. Evaluate a one-step expression that contains grouping symbols. Given a verbal phrase, identify the operation. Identify a number on a vertical or horizontal number line. Add and subtract monetary amounts, including in whole numbers (with the $.00 included). Student may use a model or drawing. Add or subtract fractions with like denominators using models (limit to halves, thirds, fourths, sixths, and eighths). Multiply a whole number by a fraction (limit to compatible numbers that result in a whole number product). Evaluate a two-step numerical expression involving grouping symbols (limit to addition and subtraction) Translate verbal phrases into simple numerical expressions (limit one-step addition or subtraction) Plot a number on a vertical or horizontal number line. Add and subtract multi-digit decimal numbers without regrouping. Add and subtract monetary amounts including dollars and cents. Student may use a model or drawing. Add or subtract fractions with unlike denominators (limit to halves, thirds, fourths, sixths, and use visual models). Multiply a whole number by a fraction. Evaluate two-step numerical expressions involving grouping symbols (i.e., parentheses, brackets, braces; limit to addition and subtraction). Translate verbal phrases into simple numerical expressions. Identify an ordered pair on a coordinate plane. Page 10
5.G.1 a. The x- and y-axes are perpendicular number lines that intersect at 0 (the origin) Recognize point on a number line (limit to numbers greater than 0). Identify a number on a vertical or horizontal number line. Plot a number on a vertical or horizontal number line. Identify an ordered pair on a coordinate plane. 5.G.1 b. Any point on the coordinate plane can be represented by its coordinates. Recognize a point on a number line (limit to numbers greater than 0). Identify a number on a vertical or horizontal number line. Plot a number on a vertical or horizontal number line. Identify an ordered pair on a coordinate plane. 5.G.1 c. The first number in an ordered pair is the x- coordinate and represents the horizontal distance from the origin. Recognize a point on a number line (limit to numbers greater than 0). Identify a number on a vertical or horizontal number line. Plot a number on a vertical or horizontal number line. Identify an ordered pair on a coordinate plane. 5.G.1 d. The second number in an ordered pair is the y- coordinate and represents the vertical distance from the origin. 5.G.2 Plot points in the first quadrant. Recognize a point on a number line (limit to numbers greater than 0). Recognize a point. Identify a number on a vertical or horizontal number line. Recognize intersecting lines/line segments. Plot a number on a vertical or horizontal number line. Recognize perpendicular lines/line segments. Identify an ordered pair on a coordinate plane. Plot a point on a map given the x and y variables. 5.MDA.1 Convert measurements within a single system of measurement customary (i.e., in., ft., yd., min., hr.) or metric (i.e., cm, m, km, ml, L) from a larger to a smaller unit. Recognize measurable attributes. Make direct comparison of two lengths. Make direct comparison of two masses. Use an appropriate tool for measuring length using inches; use an appropriate tool for measuring length using feet; use an appropriate tool for measuring mass in pounds; use an appropriate tool for measuring mass in ounces. Convert measurements within a single system of measurement. Page 11
5.MDA.4 Differentiate among perimeter, area, and volume, and identify which application is appropriate for a given situation. Recognize measureable attributes. Calculate perimeter by adding all the side lengths. Calculate the area by counting the square units. Solve word problems involving perimeter of polygons. Solve word problems by using perimeter, area, or volume. Page 12
Grade 6 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 6.NS.2 Fluently divide multidigit whole numbers limited to four-digit dividends and two-digit divisors using a standard algorithmic approach. 6.NS.3 Fluently add and subtract multi-digit decimal numbers to the hundredths place using a standard algorithmic approach. 6.NS.4 Find common factors and multiples using two whole numbers up to 50 for factors, and less than or equal to 10 for multiples. 6.NS.5 Understand that the positive and negative representations of a number are opposites in direction and value. Use integers to represent quantities in realworld situations. 6.NS.6 Plot integers on number lines and ordered pairs on the coordinate plane. Demonstrate the concept of division. Identifies whole and part. Identify fact families of a number using multiplication. Given a real-world context, identify the value of the situation (limit to positive numbers under 15). Identify a number on a vertical or horizontal number line. Apply the relationship between multiplication and division. Identify a whole number when presented in monetary form. Identify a decimal when presented in monetary form. Find the factors of a number (limit to fact families under 50). Given a real-world context, identify the value of the situation (limit to positive numbers under 100). Plot a number on a vertical or horizontal number line. Divide by 1, 2, 3, 4, and/or 5. Add and subtract monetary amounts including in whole numbers (with the $.00 included); student may use a model or drawing. Given the factors of two numbers, identify the common factors (for two whole numbers up to 50 and multiples of 5 or 10). Given a real-world context, identify whether the value in the situation is positive, negative, or zero. Identify an ordered pair on a coordinate plane. Divide by numbers up to and including 10. Add and subtract multi-digit decimal numbers without regrouping. Add and subtract monetary amounts including the dollar and cents; student may use a model or drawing. Find common factors for whole numbers up to 50 and less than or equal to 10 for multiples. Given a real-world context, identify the value of the situation which may include negative numbers. Plot an ordered pair on a coordinate plane. Page 13
6.NS.7 a. Interpret statements using equal to (=) and not equal to ( ). 6.NS.7 b. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. 6.NS.7 c. Use concepts of equality and inequality to write and explain real-world and mathematical situations. 6.NS.7 d. Understand that absolute value represents a number s distance from zero on the number line and use the absolute value of an integer number to represent real-world situations. Identify if two statements are equal (=) and not equal ( ). Identify if two statements are equal (=) and not equal ( ). Identify if two statements are equal (=) and not equal ( ). Identify if two statements are equal (=) and not equal ( ). Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=), to describe their locations on the number line. Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. Given two points on a number line, identify a statement using less than (<), greater than (>), and equal to (=) to describe their locations on the number line. Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. Given a real-world or mathematical situation, identify a statement of equality or inequality that describes it. Given a real world or mathematical situation, identify a statement of equality or inequality that describes it. Given a real world or mathematical situation, identify a statement of equality or inequality that describes it. Identify the absolute value of a number as the distance from zero on a number line. Identify the absolute value of a number as the distance from zero on a number line. Identify the absolute value of a number as the distance from zero on a number line. Identify the absolute value of a number as the distance from zero on a number line. Page 14
6.NS.9 Explore and translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100. 6.RP.1 Understand the concept of a ratio as the relationship between two quantities, including part to part and part to whole. 6.EE.1 Write numerical expressions involving whole numbers using the Order of Operations. 6.EE.2 Identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and variable. 6.EE.7 Identify linear equations for real-world situations. Identify a whole number. Identify a ratio. Given an equation, identify the symbols for the four functions (+, -, x, divide). Distinguish between a number and a letter. Recognize that an unknown value can be represented by a variable. Identify the definition of a rational number. Identify a ratio that matches a context. Given an equation, identify the first step for order of operations. Identify an algebraic expression. Identify the relationship between two variables. Identify multiple representations of a rational number. Understand the concept of a ratio as the relationship between two quantities (limit to part to whole). Given an equation, identify the order of operations. Identify the parts of an expression using mathematical terminology (limit to term and variable). Identify a situation where the variables create an increasing linear equation (e.g. The more hours you work, the higher your paycheck; the further away your destination, the longer the bus ride). Translate multiple representations of rational numbers (fractions, decimal numbers, and percentages). Fractions should be limited to those with denominators of 2, 3, 4, 5, 8, 10, and 100. Understand the concept of a ratio as the relationship between two quantities, including part to part and part to whole. Write numerical expressions involving whole numbers using the Order of Operations. Identify parts of algebraic expressions using mathematical terminology, including term, coefficient, constant, and variable. Identify linear equations related to wages, finances, time, and distance. Page 15
6.GM.1 Find the area of right triangles and rectangles. 6.DS.1 Find the mean, median, mode, and range. Identify a triangle. Find the largest/smallest number in a data set. Identify a triangle that has a right angle. Put a data set in order from least to greatest. Find the area of a rectangle given the side lengths and tiles. Determine the middle point of a collection of objects. Find the area of right triangles and rectangles when given side lengths. Identify the median and/or range of a data set. Page 16
Grade 7 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 7.NS.1 Extend prior knowledge of operations with positive rational numbers to add and to subtract all rational numbers and represent the sum or difference on a number line. 7.NS.2 Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers. 7.NS.3 Apply the concepts of all four operations with positive rational numbers to solve one-step, real-world and mathematical problems. Identify a whole number or a fraction. Identify a whole number or a fraction. Apply the concepts of the operations of addition and subtraction with positive rational numbers to solve one-step, real-world and mathematical problems. Convert a whole number into a fraction. Convert a whole number into a fraction. Apply the concepts of the operations of multiplication and division with positive rational numbers to solve one-step, real-world and mathematical problems. Extend prior knowledge of operations with positive rational numbers to add and subtract all rational numbers. Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers. Apply the concepts of all four operations with positive rational numbers to solve one-step, real-world and mathematical problems. Extend prior knowledge of operations with positive rational numbers to add and subtract all rational numbers and represent the sum or difference on a number line. Extend prior knowledge of operations with positive rational numbers to multiply and divide all rational numbers and represent the result on a number line. Apply the concepts of all four operations with positive rational numbers to solve two-step, real-world and mathematical problems. Page 17
7.NS.4 Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), less than or equal to ( ), greater than or equal to ( ), and equal to (=) as relative locations on the number line. 7.NS.5 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers). Exclude the conversion of repeating decimal numbers to fractions. 7.RP.2 Identify proportional relationships given multiple representations, including tables, graphs, and realworld situations. a. Determine when two quantities are in a proportional relationship. e. Identify the graph of a proportional relationship in a real-world situation. Understand and apply the concepts of comparing and ordering whole numbers on a number line. Identify same and different fractions or decimal numbers from pictorial representations. Identify equivalent relationships in real-world situations. Understand and apply the concepts of comparing and ordering whole numbers on a number line. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. Identify equivalent fractions and decimal numbers up to 100. Exclude the conversion of repeating decimal numbers to fractions. Identify proportional relationships in real-world situations. Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), and equal to (=) as relative locations on the number line. Extend prior knowledge to translate among fractions and decimal numbers up to 100. Exclude the conversion of repeating decimal numbers to fractions. Identify proportional relationships given multiple representations, including tables, graphs, and realworld situations. a. Determine when two quantities are in a proportional relationship. Understand and apply the concepts of comparing and ordering rational numbers on a number line. Interpret statements using less than (<), greater than (>), less than or equal to ( ), greater than or equal to ( ), and equal to (=) as relative locations on the number line. Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers). Exclude the conversion of repeating decimal numbers to fractions. Identify proportional relationships given multiple representations, including tables, graphs, and real-world situations. a. Determine when two quantities are in a proportional relationship. e. Identify the graph of a proportional relationship in a real-world situation. Page 18
7.RP.3 Solve real-world and mathematical problems involving ratios and percentages. 7.EE.1 Apply mathematical properties (e.g., commutative, associative) to simplify linear algebraic expressions with whole number coefficients. 7.EE.3 Extend previous understanding of Order of Operations to solve multistep real-world and mathematical problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol. 7.GM.6 Understand that the concept of area applies to two-dimensional figures. Understand that the concepts of volume applies to three-dimensional figures. Understand part and whole relationships. Apply mathematical commutative property of addition. Identify a mathematical operation by its symbol. Understand the difference between two dimensional and three dimensional figures. Solve real-world problems involving percentages. Apply mathematical commutative property of addition and multiplication. Know the order of operations in a mathematical expression. Understand the concept of area. Understand the concept of volume. Solve real-world problems involving ratios and percentages. Apply mathematical commutative property to simplify linear algebraic expressions with whole number coefficients. Extend previous understanding of Order of Operations to solve twostep real-world problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol. Understand that the concept of area applies to twodimensional figures. Understand that the concepts of volume applies to three-dimensional figures. Solve real-world and mathematical problems involving ratios and percentages. Apply mathematical properties (e.g., commutative, associative) to simplify linear algebraic expressions with whole number coefficients. Extend previous understanding of Order of Operations to solve multistep real-world and mathematical problems involving whole numbers. Exclude exponents and fraction bars as a grouping symbol. Understand that the concept of area applies to twodimensional figures. Understand that the concepts of volume applies to threedimensional figures. Understand which formula to use to calculate either area or volume. Page 19
7.DS.1 Understand that a sample is a subset of a population. Distinguish between populations and samples. Distinguish between random and nonrandom samples. 7.DS.2 Draw inferences about a population by collecting random samples. 7.DS.4 Use the numerical measures of center (mean, median, mode, and range). 7.DS.5 Understand that probability measures likelihood of a chance event occurring. Distinguish between a whole and a part. Determine if it is a random sample. Determine the middle point of a collection of objects. Recognize the outcome of an event. Determine if it is a population or a sample. Identify a statement about a given random sample. Identify the median of a data set. Identify if an event is possible or impossible. Understand that a sample is a subset of a population. Identify populations and samples. Identify random and nonrandom samples. Draw inferences about a population when given random samples. Use the numerical measures of center (mean and median). Understand that probability measures likelihood of a chance event occurring. Understand that a sample is a subset of a population. Distinguish between populations and samples. Distinguish between random and nonrandom samples. Draw inferences about a population by collecting random samples. Use the numerical measures of center (mean, median, mode, and range). Determine the probability of simple events. Page 20
Grade 8 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard 8.NS.1 Recognize the differences between rational and irrational numbers. Understand that all real numbers have a decimal expansion. 8.NS.2 Estimate the value of irrational and rational numbers by plotting them on a number line. 8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions. Identify whole numbers and fractions. Plot whole numbers and fractions on a number line. Identify fractions. Identify rational numbers. Plot rational numbers on a number line. Translate fractions with the denominators 2, 4, 6, 8, and 10 into decimals. Recognize the differences between rational and irrational numbers. Plot irrational and rational numbers on a number line. Translate among multiple representations of rational numbers (fractions and decimal numbers). Exclude the conversion of repeating decimal numbers to fractions. Recognize the differences between rational and irrational numbers. Understand that all real numbers have a decimal expansion. Estimate the value of irrational and rational numbers by plotting them on a number line. Translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Exclude the conversion of repeating decimal numbers to fractions. Page 21
8.F.1 Understand that a function assigns to each input exactly one output. Determine if a relation is a function using multiple representations, including tables, graphs and equations. Graph a function from a table of x and y values. Extend the knowledge of the coordinate plane to use the set of ordered pairs of that function. 8.F.2 Compare two functions, including tables, graphs, and equations, in order to draw conclusions. 8.F.4 Understand that the slope is the constant rate of change and the y-intercept is the point where x = 0. Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation. 8.EE.1 Understand exponents to simplify numerical expressions that include integer exponents. Identify a point. Identify the slope or intercepts of a function in graph form. Identify a line on a graph. Identify repeated multiplication (4x4x4) as the exponent notation (4 3 ). Graph a point when given an ordered pair of numbers. Identify the slope and intercepts of a function given in equation form. Understand that slope is related to the direction of the line. Expand exponents into repeated multiplication. Graph a function from a table of x and y values. Compare the slopes of two functions given in equation form (slope intercept form). Understand that the slope is the constant rate of change, and the y-intercept is the point where x = 0. Understand exponents to simplify numerical expressions. Generate ordered pairs from two distinct numerical patterns. Extend a symbolic pattern by applying the rule. Compare two functions, including tables, graphs and equations in order to draw conclusions. Understand that the slope is the constant rate of change, and the y-intercept is the point where x = 0. Interpret the meaning of the slope and the y-intercept of a linear function in the context of the situation Understand exponents to simplify numerical expressions that include integer exponents. Page 22
8.EE.2 Investigate concepts of square roots. 8.EE.5 Compare two different proportional relationships using tables and graphs. 8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools to recognize congruence. 8.DS.1 Recognize patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, or no correlation). Understand multiplication as repeated addition. Identify a table or graph. Recognize when twodimensional shapes are the same. Identify a point. Understand multiplication facts of whole numbers with products up to 100. Compare two relationships using tables and graphs Recognize congruent figures. Graph points when given an ordered pair of numbers. Understand how to square a number. Compare two different proportional relationships using tables and graphs. Investigate the properties of rigid transformations (rotations, reflections, translations). Recognize patterns observed on a scatter plot, including clustering and outliers. Understand that the square root is the inverse of squaring a number. Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions. Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools to recognize congruence. Recognize patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, or no correlation). Page 23
Grade 11 Prioritized Standard Level 1: Foundational Level 2: Emerging Level 3: Meets Standard Level 4: Exceeds Standard A1.AAPR.1 Add and subtract polynomials (limit to linear). A1.ACE.1 Solve linear equations with one variable. A1.AREI.1 Understand that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original. A1.AREI.6 Solve systems of linear equations graphically focusing on pairs of linear equations in two variables. A1.AREI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. A1.AREI.12 Graph the solutions to a simple inequality with one variable on a number line. Add two like terms (limited to constants). Given a linear equation, identify parts of the equation (variable, constant, and coefficient). Determine if two expressions are equal (2x3, 3x2, commutative property, associative property). Identify a set of lines that intersect. Identify a point in the first quadrant. Identify a point on the number line. Add and subtract like terms (limited to constants). Solve an equation written with the variable isolated on the left side. Identify the possible first step in solving an equation. Identify the point at which a given set of lines intersect. Identify an equation in the first quadrant. Identify an inequality on the number line (limit to greater than and less than, limit to positive number line starting at zero). Add and subtract like terms that may include a variable. Solve a linear equation with one variable with one step (addition, subtraction). Identify the possible next step in solving an equation. Given the graph of one equation and a simple equation, identify the graph that models the solution. Identify the graph of an equation in two variables that models the set of all its solutions plotted in the coordinate plane (limit to the first quadrant). Identify an inequality on the number line (where the solution is a positive number but the number line may include negative numbers). Add and subtract like terms with simple expressions. Solve linear equation with one variable. Understand that the steps taken when solving simple equations in one variable create new equations that have the same solution as the original. Solve systems of linear equations, graphically focusing on pairs of linear equations in two variables. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. Identify a simple inequality with one variable on a number line (include greater than or equal to). Page 24
A1.ASE.1 Determine the meanings of coefficients, variables, terms, and expressions based on their real-world contexts. A1.FIF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. A1.FIF.4 Recognize features of a linear function in graphical form (e.g., slope, intercepts; if the function is increasing, decreasing, constant, positive, or negative). A1.FIF.7 Graph linear functions using their key features. A1.NQ.1 Choose the appropriate labels, units, and scales when constructing graphs. A1.NRNS.1 Evaluate square roots of perfect squares. Given an expression, identify a part (variable, term). Given a set of table values, identify the set of x-values. Given a key feature (increasing, decreasing, or constant), identify the graph. Identify whether a given graph is increasing, decreasing, or constant. Given data and a context, identify an appropriate title for a graph of the data. Understand multiplication facts of whole numbers with products up to 100. Identify the meaning of the unknown in a real-world context. Given a table of values, identify a possible missing x- value (so that an x-value does not repeat). Given an intercept of the graph, identify the graph. Given a graph of a linear function, identify the x- intercept. Given context, identify a graph with correct labels. Understand how to square a number. Given a real-world context and a variable, determine what the variable represents. Identify if a relation given in table form is a function. Given a description of a function, identify the graph (positive slope, negative slope, constant, given y- intercept, limit to first quadrant). Given a graph of a linear function in the first quadrant, identify features of the graph (positive slope, negative slope, constant, intercepts). Given a data set, identify the appropriate units for a graph of the data. Understand that the square root is the inverse of squaring a number. Determine the meanings of coefficients, variables, terms, and expressions based on their real-world contexts. Identify the domain and range of a given function. Given the slope and intercept of a function, identify its graph. Given a graph of a linear function, identify the slope and intercepts. Given a data set, identify an appropriate scale for a graph of the data. Evaluate square roots of perfect squares. Page 25
A1.SPID.6 Identify the general form of a given data set as linear or non-linear. Identify a graph that is a straight line. Identify a data set that can be modeled as a straight line. Identify a data set that is linear. Identify the general form of a given data set as linear or non-linear. Page 26